I did not know I violated some rules.
This was the only picture I found that showed my toilet with this short 'pipe'.

What is your opinion on Danco Perfect Seal?
My flange is not level. It is about 1 / 8 '' (or little bit more) below the tiles on the back and about 1 / 8 '' (or little bit more) above the tiles on front. The toilet I am replacing had a leak, so I am wondering what kind of seal should I use now to be safe.

A wax seal, maybe a jumbo, should work fine. Keep in mind, though, that ANY rocking of the toilet after it is set will likely break the wax seal - you MUST shim the toilet so it doesn't rock when you set it onto the wax. The wax is NOT springy, and if it rocks one way, compressing the wax, when it rocks back the other, you'll now have a gap that can leak. WHen you set the toilet, you should be able to feel the wax being compressed...if you don't, you may need a thicker wax ring or to fix the flange's position.

A look into the bowl of any of these confirms that there is no opening where these tubes connect at the beginning of the trapway. Could they be there for structural support of the wet clay while it's being fired?